2022 |
Victor, Stéphane; Mayoufi, Abir; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). Résumé | Liens | BibTeX | Étiquettes: Continous time, Continuous time systems, Fractional model, Fractional systems, Instrumental variables, Intelligent systems, Monte Carlo methods, Multiple input single output systems, Multiple inputs single outputs, Optimization, Optimization algorithms, Order estimation, Order optimizations, Parameter estimation, Religious buildings, System-identification @article{Victor2022b,This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis. © 2022 Elsevier Ltd |
Yakoub, Zaineb; Naifar, Omar; Amairi, Messaoud; Chetoui, Manel; Aoun, Mohamed; Makhlouf, Abdellatif Ben A Bias-Corrected Method for Fractional Linear Parameter Varying Systems Article de journal Dans: Mathematical Problems in Engineering, vol. 2022, 2022, (Cited by: 1; All Open Access, Gold Open Access). Résumé | Liens | BibTeX | Étiquettes: Bias correction, Correction techniques, Fractional model, Fractional order, Identification algorithms, LeastSquare algorithm, Linear parameter varying systems, Linear programming, Linear systems, Nelder-Mead simplex methods, Performance, Reliable results @article{Yakoub2022e,This paper proposes an identification algorithm for the fractional Linear Parameter Varying (LPV) system considering noisy scheduling and output measurements. A bias correction technique is provided in order to compensate for the bias caused by the least squares algorithm. This approach was created to estimate either coefficients or fractional-order differentiation, and it has been proven to produce unbiased and reliable results. The suggested method’s performance is assessed by the identification of two fractional models and was compared with Nelder-Mead Simplex method. © 2022 Zaineb Yakoub et al. |
Victor, Stéphane; Mayoufi, Abir; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). Résumé | Liens | BibTeX | Étiquettes: Continous time, Continuous time systems, Fractional model, Fractional systems, Instrumental variables, Intelligent systems, Monte Carlo methods, Multiple input single output systems, Multiple inputs single outputs, Optimization, Optimization algorithms, Order estimation, Order optimizations, Parameter estimation, Religious buildings, System-identification @article{Victor2022,This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis. © 2022 Elsevier Ltd |
2020 |
Mayoufi, Abir; Victor, Stéphane; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed vol. 53, 2020, (Cited by: 1; All Open Access, Bronze Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Fractional model, Fractional model identification, Instrumental variables, Monte Carlo methods, Multiple input single outputs, Order estimation, Refined instrumental variables, Single input single output @conference{Mayoufi20203701b,This paper proposes an instrumental variable approach for continuous-time system identification using fractional models with multiple input single output context. This work is an extension of the simplified refined instrumental variable approach (srivcf) developed for single input-single output fractional model identification (Malti et al. (2008a); Victor et al. (2013)) to the multiple input-single output case. Monte Carlo simulation analysis is used to demonstrate the performance of the proposed approach. A study is then provided to motivate differentiation order estimation, and more specifically, commensurate order estimation. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0) |
Mayoufi, Abir; Chetoui, Manel; Victor, Stephans; Aoun, Mohamed; Malti, Rachid A comparison between two methods for MISO fractional models estimation Conférence 2020, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Comparative studies, Fractional model, Fractional order, Instrumental variables, Linear coefficients, Monte Carlo methods, Multiple input single output systems, Numerical methods, Output errors @conference{Mayoufi2020446b,This paper proposes two new methods for multiple input-single output system identification with fractional models: The instrumental variable based method and the output-error based method. The fractional orders are supposed known and the linear coefficients are estimated. A comparative study between the developed methods is illustrated via a numerical example. Monte Carlo simulations are used to demonstrate the efficiency of the two methods. © 2020 IEEE. |
Mayoufi, Abir; Victor, Stéphane; Malti, Rachid; Chetoui, Manel; Aoun, Mohamed vol. 53, 2020, (Cited by: 1; All Open Access, Bronze Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Continuous time systems, Continuous-time, Fractional model, Fractional model identification, Instrumental variables, Monte Carlo methods, Multiple input single outputs, Order estimation, Refined instrumental variables, Single input single output @conference{Mayoufi20203701,This paper proposes an instrumental variable approach for continuous-time system identification using fractional models with multiple input single output context. This work is an extension of the simplified refined instrumental variable approach (srivcf) developed for single input-single output fractional model identification (Malti et al. (2008a); Victor et al. (2013)) to the multiple input-single output case. Monte Carlo simulation analysis is used to demonstrate the performance of the proposed approach. A study is then provided to motivate differentiation order estimation, and more specifically, commensurate order estimation. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0) |
Mayoufi, Abir; Chetoui, Manel; Victor, Stephans; Aoun, Mohamed; Malti, Rachid A comparison between two methods for MISO fractional models estimation Conférence 2020, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Comparative studies, Fractional model, Fractional order, Instrumental variables, Linear coefficients, Monte Carlo methods, Multiple input single output systems, Numerical methods, Output errors @conference{Mayoufi2020446,This paper proposes two new methods for multiple input-single output system identification with fractional models: The instrumental variable based method and the output-error based method. The fractional orders are supposed known and the linear coefficients are estimated. A comparative study between the developed methods is illustrated via a numerical example. Monte Carlo simulations are used to demonstrate the efficiency of the two methods. © 2020 IEEE. |
2015 |
Yakoub, Z.; Amairi, M.; Chetoui, M.; Aoun, M. On the Closed-Loop System Identification with Fractional Models Article de journal Dans: Circuits, Systems, and Signal Processing, vol. 34, no. 12, p. 3833 – 3860, 2015, (Cited by: 20). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Closed loop systems, Closed loop transfer function, Closed loops, Fractional model, Identification (control systems), Information criterion, Instrumental variable methods, Instrumental variables, Intelligent systems, Least Square, Monte Carlo methods, Non-linear optimization algorithms, Nonlinear programming, Optimization, Religious buildings @article{Yakoub20153833b,In this paper, the fractional closed-loop system identification problem is addressed. Using the indirect approach, which supposes the knowledge of the controller, both coefficients and fractional orders of the process are estimated. The optimal instrumental variable method combined with a nonlinear optimization algorithm is handled to identify the fractional closed-loop transfer function. Also, two techniques are used for model selection the Akaike’s information criterion and the $$R_T^2$$RT2 criterion. The performances of the proposed scheme are illustrated by a numerical example via Monte Carlo simulation and by real electronic system identification. © 2015, Springer Science+Business Media New York. |
2014 |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: Calculations, Closed loop systems, Closed loops, Differentiation (calculus), Fractional calculus, Fractional model, Identification (control systems), Least Square, Least squares approximations, Least squares techniques, Open-loop process, Religious buildings, State-variable filters @conference{Yakoub2014c,This paper deals with fractional closed-loop system identification using the indirect approach. Firstly, all differentiation orders are supposed known and only the coefficients of the closed-loop fractional transfer function are estimated using two methods based on least squares techniques. Then, the fractional open-loop process is determined by the knowledge of the regulator. A numerical example is presented to show the effectiveness of the proposed scheme. © 2014 IEEE. |
Aribi, Asma; Farges, Christophe; Aoun, Mohamed; Melchior, Pierre; Najar, Slaheddine; Abdelkrim, Mohamed Naceur Fault detection based on fractional order models: Application to diagnosis of thermal systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, p. 3679 – 3693, 2014, (Cited by: 28). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Diagnosis, Diagnosis methods, Fault detection, Fractional model, Fractional operators, Fractional order models, Numerical analysis, Reduced precision, Single input multi outputs, Thermal phenomena, Thermal systems @article{Aribi20143679b,The aim of this paper is to propose diagnosis methods based on fractional order models and to validate their efficiency to detect faults occurring in thermal systems. Indeed, it is first shown that fractional operator allows to derive in a straightforward way fractional models for thermal phenomena. In order to apply classical diagnosis methods, such models could be approximated by integer order models, but at the expense of much higher involved parameters and reduced precision. Thus, two diagnosis methods initially developed for integer order models are here extended to handle fractional order models. The first one is the generalized dynamic parity space method and the second one is the Luenberger diagnosis observer. Proposed methods are then applied to a single-input multi-output thermal testing bench and demonstrate the methods efficiency for detecting faults affecting thermal systems. © 2014 Elsevier B.V. |
Aribi, Asma; Farges, Christophe; Aoun, Mohamed; Melchior, Pierre; Najar, Slaheddine; Abdelkrim, Mohamed Naceur Fault detection based on fractional order models: Application to diagnosis of thermal systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, p. 3679 – 3693, 2014, (Cited by: 28). Résumé | Liens | BibTeX | Étiquettes: Computer simulation, Diagnosis, Diagnosis methods, Fault detection, Fractional model, Fractional operators, Fractional order models, Numerical analysis, Reduced precision, Single input multi outputs, Thermal phenomena, Thermal systems @article{Aribi20143679,The aim of this paper is to propose diagnosis methods based on fractional order models and to validate their efficiency to detect faults occurring in thermal systems. Indeed, it is first shown that fractional operator allows to derive in a straightforward way fractional models for thermal phenomena. In order to apply classical diagnosis methods, such models could be approximated by integer order models, but at the expense of much higher involved parameters and reduced precision. Thus, two diagnosis methods initially developed for integer order models are here extended to handle fractional order models. The first one is the generalized dynamic parity space method and the second one is the Luenberger diagnosis observer. Proposed methods are then applied to a single-input multi-output thermal testing bench and demonstrate the methods efficiency for detecting faults affecting thermal systems. © 2014 Elsevier B.V. |
2012 |
Aoun, Mohamed; Najar, Slaheddine; Abdelhamid, Moufida; Abdelkrim, Mohamed Naceur Continuous fractional Kalman filter Conférence 2012, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: Continuous time, Fractional differentiation, Fractional model, Kalman filters, Linear systems, Numerical example, State estimation, Suboptimal filter @conference{Aoun2012b,This paper develops a new Kalman filter for linear systems described with continuous time fractional model. It extends the classical Kalman filter to deals with fractional differentiation. It is called continuous fractional Kalman Filter. The algorithm of the new filter is detailed and a suboptimal filter can be deduced. A numerical example illustrates the state estimation of a fractional model with the new filter. © 2012 IEEE. |
Amairi, Messaoud; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur Set membership parameter estimation of linear fractional systems using parallelotopes Conférence 2012, (Cited by: 11). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Fractional model, Fractional systems, Parameter estimation, Set-membership, Time domain @conference{Amairi2012c,The paper deals with set-membership parameter estimation of fractional models in the time-domain. In such a context, the noise is supposed to be unknown-but-bounded with a priori known bounds. The proposed algorithm computes the set of all feasible parameters represented by a parallelotop. Simulation results and performance comparaison with the ellipsoidal approach are also given. © 2012 IEEE. |
Aoun, Mohamed; Najar, Slaheddine; Abdelhamid, Moufida; Abdelkrim, Mohamed Naceur Continuous fractional Kalman filter Conférence 2012, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: Continuous time, Fractional differentiation, Fractional model, Kalman filters, Linear systems, Numerical example, State estimation, Suboptimal filter @conference{Aoun2012,This paper develops a new Kalman filter for linear systems described with continuous time fractional model. It extends the classical Kalman filter to deals with fractional differentiation. It is called continuous fractional Kalman Filter. The algorithm of the new filter is detailed and a suboptimal filter can be deduced. A numerical example illustrates the state estimation of a fractional model with the new filter. © 2012 IEEE. |
2010 |
Amairi, Messaoud; Najar, Slaheddine; Aoun, Mohamed; Abdelkrim, M. N. Guaranteed output-error identification of fractional order model Conférence vol. 2, 2010, (Cited by: 13). Résumé | Liens | BibTeX | Étiquettes: Fractional differentiation, Fractional model, Fractional order, Fractional order models, Fractional-order systems, Global optimization, Global optimization techniques, Guaranteed convergence, Identification (control systems), Interval analysis, Optimization, System identifications @conference{Amairi2010246b,A global optimization technique for identifying an output-error fractional order model is proposed. The proposed technique use a modified version of Hansen algorithm. It is capable of estimating the fractional orders and the parameters, with guaranteed convergence. The technique is applied to identify a fractional order system in deterministic and stochastic context. © 2010 IEEE. |
2006 |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Application programs, Battery management systems, Charging (batteries), Estimation methods, Fractional behavior, Fractional model, Fractional systems, Identification (control systems), Lead acid batteries, Operating temperature, Religious buildings, State-of-charge estimation, Unknown state, Validation test @conference{Sabatier2006296b,This paper deals with the application of fractional system identification to lead acid battery state of charge estimation. Fractional behavior of lead acid batteries is justified. A fractional system identification method recently developed is presented and a new fractional model of the battery is proposed. Based on parameter variations of this model, a state of charge estimation method is presented. Validation tests of this method on unknown state of charge are carried out. These validation tests highlights that the proposed estimation method gives a state of charge estimation with an error less than 5% whatever the operating temperature. |
Sabatier, Jocelyn; Aoun, Mohamed; Oustaloup, Alain; Grégoire, Gilles; Ragot, Franck; Roy, Patrick Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Application programs, Battery management systems, Charging (batteries), Estimation methods, Fractional behavior, Fractional model, Fractional systems, Identification (control systems), Lead acid batteries, Operating temperature, Religious buildings, State-of-charge estimation, Unknown state, Validation test @conference{Sabatier2006296,This paper deals with the application of fractional system identification to lead acid battery state of charge estimation. Fractional behavior of lead acid batteries is justified. A fractional system identification method recently developed is presented and a new fractional model of the battery is proposed. Based on parameter variations of this model, a state of charge estimation method is presented. Validation tests of this method on unknown state of charge are carried out. These validation tests highlights that the proposed estimation method gives a state of charge estimation with an error less than 5% whatever the operating temperature. |
2004 |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117b,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
2002 |
Aoun, Mohamed; Malti, Rachid; Cois, Olivier; Oustaloup, Alain System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). Résumé | Liens | BibTeX | Étiquettes: Automation, Continuous time systems, Fractional differentiation, Fractional model, Fractional order, Hammerstein model, Hammerstein-type models, Identification (control systems), Identification method, Linear systems, Non-linear modelling, Nonlinear systems, Riemann-liouville definitions @conference{Aoun2002265b,Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC. |
Aoun, Mohamed; Malti, Rachid; Cois, Olivier; Oustaloup, Alain System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). Résumé | Liens | BibTeX | Étiquettes: Automation, Continuous time systems, Fractional differentiation, Fractional model, Fractional order, Hammerstein model, Hammerstein-type models, Identification (control systems), Identification method, Linear systems, Non-linear modelling, Nonlinear systems, Riemann-liouville definitions @conference{Aoun2002265,Identification of continuous-time non-linear systems characterised by fractional order dynamics is studied. The Riemann-Liouville definition of fractional differentiation is used. A new identification method is proposed through the extension of Hammerstein-type models by allowing their linear part to belong to the class of fractional models. Fractional models are compact and so are used here to model complex dynamics with few parameters. Copyright © 2002 IFAC. |
Publications
2022 |
System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). |
A Bias-Corrected Method for Fractional Linear Parameter Varying Systems Article de journal Dans: Mathematical Problems in Engineering, vol. 2022, 2022, (Cited by: 1; All Open Access, Gold Open Access). |
System identification of MISO fractional systems: Parameter and differentiation order estimation Article de journal Dans: Automatica, vol. 141, 2022, (Cited by: 10). |
2020 |
vol. 53, 2020, (Cited by: 1; All Open Access, Bronze Open Access, Green Open Access). |
A comparison between two methods for MISO fractional models estimation Conférence 2020, (Cited by: 0). |
vol. 53, 2020, (Cited by: 1; All Open Access, Bronze Open Access, Green Open Access). |
A comparison between two methods for MISO fractional models estimation Conférence 2020, (Cited by: 0). |
2015 |
On the Closed-Loop System Identification with Fractional Models Article de journal Dans: Circuits, Systems, and Signal Processing, vol. 34, no. 12, p. 3833 – 3860, 2015, (Cited by: 20). |
2014 |
Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). |
Fault detection based on fractional order models: Application to diagnosis of thermal systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, p. 3679 – 3693, 2014, (Cited by: 28). |
Fault detection based on fractional order models: Application to diagnosis of thermal systems Article de journal Dans: Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, p. 3679 – 3693, 2014, (Cited by: 28). |
2012 |
Continuous fractional Kalman filter Conférence 2012, (Cited by: 4). |
Set membership parameter estimation of linear fractional systems using parallelotopes Conférence 2012, (Cited by: 11). |
Continuous fractional Kalman filter Conférence 2012, (Cited by: 4). |
2010 |
Guaranteed output-error identification of fractional order model Conférence vol. 2, 2010, (Cited by: 13). |
2006 |
Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). |
Estimation of lead acid battery state of charge with a novel fractional model Conférence vol. 2, no. PART 1, 2006, (Cited by: 6; All Open Access, Bronze Open Access). |
2004 |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). |
2002 |
System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). |
System identification using fractional hammerstein models Conférence vol. 15, no. 1, 2002, (Cited by: 23). |